Introduction to Acoustics

as the result of coupling of a significant fraction of
the incident sound energy into ground-borne Rayleigh
waves.
Numerical theory has also been used to explore the
consequences of this coupling for the excess attenuation
of low-frequency sound above ground [4.82].
Figure 4.12 shows the excess attenuation spectra predicted
for source height 2 m, receiver height 0.1m and
horizontal range of 6.3 km over a layered ground profile
corresponding to Table 4.1 (assumed a speed of sound in
airof329m/s) and by classical theory for a point source
above an impedance (locally reacting) plane (4.22) using
the impedance calculated for a 0.018 ◦ grazing angle
(Zeff, broken lines in Fig. 4.9).
4.7 Attenuation Through Trees and Foliage
A mature forest or woodland may have three types of
influence on sound. First is the ground effect. This is
particularly significant if there is a thick litter layer of
partially decomposing vegetation on the forest floor. In
such a situation the ground surface consists of a thick
highly porous layer with rather low flow resistivity, thus
giving a primary excess attenuation maximum at lower
frequencies than observed over typical grassland. This is
similar to the effect, mentioned earlier, over snow. Secondly
the trunks and branches scatter the sound out of
the path between source and receiver. Thirdly the foliage
Attenuation (dB re 2m)
25
Ground effect
200–300 Hz
20
15
10
5
0
Summer
maximum
Foliage
effect
> 1 kHz
–5
0.1 1
10
Frequency (kHz)
Sound Propagation in the Atmosphere 4.7 Attenuation Through Trees and Foliage 129
Summer
minimum
Winter
mean
The predictions show a significant extra attenuation
for 2–10 Hz. The predictions also indicate that, for an
assumed speed of sound in air of 329 m/s, and, apart
from an enhancement near 2 Hz, the excess attenuation
spectrum might be predicted tolerably well by using
modified classical theory instead of a full poro-elastic
layer calculation.
It is difficult to measure the surface impedance of
the ground at low frequencies [4.83, 84]. Consequently
the predictions of significant ground elasticity effects
have been validated only by using data for acoustic-toseismic
coupling, i. e., by measurements of the ratio of
ground surface particle velocity relative to the incident
sound pressure [4.82].
attenuates the sound by viscous friction. To predict the
total attenuation through woodland, Price et al. [4.85]
simply added the predicted contributions to attenuation
for large cylinders (representing trunks), small cylinders
(representing foliage), and the ground. The predictions
are in qualitative agreement with their measurements,
but it is necessary to adjust several parameters to obtain
quantitative agreement. Price et al. found that foliage
has the greatest effect above 1 kHz and the foliage attenuation
increased in approximately a linear fashion with
frequency. Figure 4.13 shows a typical variation of at-
Attenuation (dB/m)
0.8
0.6
0.4
0.2
0
1�10 3
0.7(logf) – 2.03
0.4(logf) – 1.2
0.26(logf) – 0.75 ISO9613-2
1�10 4
Frequency (Hz)
Fig. 4.13 (Left) Measured attenuation through alternate bands of Norway spruce and oak (planted in 1946) with hawthorn,
roses and honeysuckle undergrowth; visibility less than 24 m. (Right) Linear fits to attenuation above 1 kHz in mixed
conifers (squares), mixed deciduous summer (circles) and spruce monoculture (diamonds). Also shown is the foliage
attenuation predicted according to ISO 9613-2. (After [4.24])
Part A 4.7